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Another Look at Estimating Reliable Profit Indicators IN tRANSFER pRICING

Posted by Ednaldo Silva

We take another look that computing profit indicators using restricted data samples can lead to unreliable measures of arm’s length taxable income to benchmark controlled inter-group transactions. To produce reliable measures, we must change the pervasive transfer pricing practice of considering three-years of data, and consider as many individual company financial data as available.

We consider in our example the current and historical operating profit margin after depreciation of Walmart (GVKEY 11259). In Capital IQ (Compustat) mnemonics, operating profit margin after depreciation is called OMAD, which is also known as EBIT margin.

If Walmart is regarded to be comparable to a controlled tested party under the TNMM (CPM in the United Sates), computing its three-year median OMAD is not sensible because the series of annual OMAD reveal a high polynomial behavior; therefore, slicing any three years of data produces unreliable measures of Walmart’s OMAD.

To visualize our concern with computations of three-year quartiles, we plotted two curves of Walmart’s historical OMAD. The first chart shows that the OMAD series is not stationary, and that we need a higher than cubic polynomial to obtain a good fit for Walmart’s declining OMAD trend. The last three years (2018, 2017 and 2016) show an abnormal OMAD pattern--that is, a cluster of three-year data points lower than the prior historical nadir.

The second chart shows one-period differences in OMAD, which results in a near-stationary series. The third chart shows the behavior of the operating profit markup, which we estimated using equation (1) below, with increasing sample sizes, starting with three years of data and ending with 41 data pairs. On chart three, the solid red line is a Lowess curve showing the number of data years required for the estimated operating profit markup to settle down to a stable value.

We use regression analysis and estimate two measures of Walmart’s operating profit markup from which we can obtain the corresponding OMAD. The dependent variable S(t) is Net Sales in year t = 1 to 41 years, and again using Capital IQ (Compustat) mnemonics, the independent variable C(t) = COGS + XSGA + (DP – AM) is Total Costs, including depreciation (DP) but excluding the amortization of acquired intangibles (AM). 

In theory, we employ Kalecki's (1954) profit markup model:

     (1)     S(t) = λ C(t) + V(t)

where λ is the estimated operating profit markup and V(t) is a transformed random variable with mean zero and Newey-West corrected variance.

The displacement λ ± (2 × SE(λ)), where SE denotes the standard error of the regression (slope) coefficient, is used to compute a confidence interval around the estimated slope coefficient.

The net profit margin is obtained by indirect least squares from equation (1) by using the formula:

     (2)     OMAD = (λ – 1) / λ


The proof is in the pudding, and thus we consider Walmart’s 41 annual total costs and net sales data pairs from 1978 to 2018 to test whether model (1) produces a reliable measure of comparable OMAD:

     (3)     S(t) ≈ 1.0504 C(t

with the Newey-West t-statistics = 289.8 and R2 = 0.9999. The intercept is insignificant, which we regard as zero.

We estimated also one-year-differences in the regression variables, and obtained:

     (4)     ∆S(t) ≈ 1.0604 ∆C(t)

with the Newey-West t-statistics = 59.2 and R2 = 0.9925. The intercept disappears when we take the one-period difference of the dependent and independent variables.

The markup pricing model (1) is found in Kalecki (1954). However, we can obtain earlier versions of markup pricing in classical economics, and in Cournot (1838). See

Newey-West t-statistics means that we computed HAC (Heteroskedasticity and Autocorrelation Consistent) standard errors. See Green (2018), Section 20.5.2, pp. 998-999.

Regression (3) produces an OMAD = 4.8%, and regression (4) produces an OMAD = 5.7%. See equation (2). Again, this measure of OMAD excludes AM from the numerator. Measured by the higher Newey-West t-statistics, regression equation (3) shows stronger (more reliable) results than (4).

An important rule-changing implication of this exercise is that we must select profit indicators with a clear theoretical underpinning (e.g., Kalecki (1954)), and we must consider many years of data available for each selected comparable. The regression estimates of operating profit indicators using larger data samples produce more reliable arm’s length ranges of near-neighbor values than the computation of quartiles using three years of data. 


Augustin Cournot, Mathematical Principles of the Theory of Wealth, Macmillan, 1927. Original in French, 1838.

William Green, Econometric Analysis (8th edition), Pearson, 2018.

Michael Kalecki, Theory of Economic Dynamics, George Allen & Unwin, 1954. Reprinted in Michael Kalecki, Selected Essays on the Dynamics of the Capitalist Economy, Cambridge University Press, 1971, Chapter 5 (Costs and prices). An earlier version of his markup pricing equation was published in Michael Kalecki, Studies in Economic Dynamics, George Allen & Unwin, 1943, Chapter 1 (Costs and prices).


Time Series Plot of OMAD

Time Series Plot of OMAD Differences-1

Scatterplot of Markup vs Count-1


Published on Oct 19, 2019 3:05:09 PM

Ednaldo Silva (Ph.D.) is founder and managing director of RoyaltyStat. He helped draft the US transfer pricing regulations and developed the comparable profits method called TNNM by the OECD. He can be contacted at:

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Topics: Net Profit Indicator